Answer:
Each month is equally likely
Step-by-step explanation:
Given that for a recent year, the following are the numbers of homicides that occurred each month in New York City:
38, 30, 46, 40, 46, 49, 47, 50, 50, 42, 37, 37.
We have to check whether it is equally likely for each of the 12 months
Set Hypotheses as
H0: All months are equally likely
Ha: atleast two months are not equally likely
(Two tailed chisquare test at 5% significance level)
This is a test for chi square goodness of fit and so assuming H0 to be true
we divide the total equaly among 12 months as expected
Observed Expected Chi square
Jan 38 42.66666667 0.510416667
Feb 30 42.66666667 3.760416667
Mar 46 42.66666667 0.260416667
Apr 40 42.66666667 0.166666667
May 46 42.66666667 0.260416667
June 49 42.66666667 0.940104167
July 47 42.66666667 0.440104167
Aug 50 42.66666667 1.260416667
Sep 50 42.66666667 1.260416667
Oct 42 42.66666667 0.010416667
Nov 37 42.66666667 0.752604167
Dec 37 42.66666667 0.752604167
Total 512 512 10.375
df=11
p value = 0.497
Since p >0.05 our alpha we accept H0
Each month is equally likely
, which means the 
th partial sum of the series can be written as
, the geometric term vanishes, leaving you with
